ONE-POINT ALGEBRAIC GEOMETRIC CODES FROM ARTIN-SCHREIER EXTENSIONS OFHERMITIAN FUNCTION-FIELDS

Recently, Garcia and Stichtenoth proposed sequences of algebraic funct ion fields with finite constant fields such that their sequences attai n the Drinfeld-Vladut bound. In the sequences, the third algebraic fun ction fields are Artin-Schreier extensions of Hermitian function field s. On the other hand, Miura presented powerful tools to construct one- point algebraic geometric (AG) codes from algebraic function fields. I n this paper, we clarify rational functions of the third algebraic fun ction fields which correspond to generators of semigroup of nongaps at a specific place of degree one. Consequently, we show generator matri ces of the one-point AG codes with respect to the third algebraic func tion fields for any dimension by using rational functions of monomial type and rational points.